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Question

In given figure diagonal AC of a quadrilateral, ABCD bisects the angles $$\angle A$$ and $$\angle C$$. Prove that AB = AD and CB = CD.
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Solution

Since diagonal AC bisects the angles $$\angle A$$ and $$\angle C$$,

we have $$\angle BAC = \angle DAC$$ and $$\angle BCA = \angle DCA$$.

In triangles ABC and ADC, 

we have

$$\angle BAC = \angle DAC$$   (given);

$$\angle BCA = \angle DCA$$    (given);

AC = AC     (common side).

So, by ASA postulate, we have

$$\triangle BAC \cong \triangle DAC$$

$$\Rightarrow$$ BA = AD and CB = CD    (Corresponding parts of congruent triangle).

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Mathematics

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